Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int h, w;
int yv[505], xv[505];
int bsm = 1e9, by0 = -1;
int main() {
  scanf("%d %d", &h, &w);
  int g[105][105];
  for (int y = (0); y < (h); y++)
    for (int x = (0); x < (w); x++) {
      scanf("%d ", &g[y][x]);
    }
  for (int y0 = (0); y0 < (505); y0++) {
    yv[0] = y0;
    for (int x = (0); x < (w); x++) xv[x] = g[0][x] - yv[0];
    for (int y = (1); y < (h); y++) yv[y] = g[y][0] - xv[0];
    bool bad = false;
    int sm = 0;
    for (int x = (0); x < (w); x++)
      for (int y = (0); y < (h); y++)
        if (xv[x] < 0 || yv[y] < 0 || xv[x] + yv[y] != g[y][x]) {
          bad = true;
        }
    for (int x = (0); x < (w); x++) sm += xv[x];
    for (int y = (0); y < (h); y++) sm += yv[y];
    if (!bad) {
      if (sm < bsm) {
        by0 = y0;
        bsm = sm;
      }
    }
  }
  if (bsm > 1e8) bsm = -1;
  printf("%d\n", bsm);
  if (bsm != -1) {
    yv[0] = by0;
    for (int x = (0); x < (w); x++) xv[x] = g[0][x] - yv[0];
    for (int y = (1); y < (h); y++) yv[y] = g[y][0] - xv[0];
    for (int y = (0); y < (h); y++)
      for (int _ = (0); _ < (yv[y]); _++) printf("row %d\n", y + 1);
    for (int x = (0); x < (w); x++)
      for (int _ = (0); _ < (xv[x]); _++) printf("col %d\n", x + 1);
  }
}